Biostat/Biomath M257
This session introduces GPU computing in Julia.
GPUs are ubiquitous in modern computers. Following are GPUs today’s typical computer systems.
| NVIDIA GPUs | Tesla K80 | GTX 1080 | GT 650M |
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| Computers | servers, cluster | desktop | laptop |
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| Main usage | scientific computing | daily work, gaming | daily work |
| Memory | 24 GB | 8 GB | 1GB |
| Memory bandwidth | 480 GB/sec | 320 GB/sec | 80GB/sec |
| Number of cores | 4992 | 2560 | 384 |
| Processor clock | 562 MHz | 1.6 GHz | 0.9GHz |
| Peak DP performance | 2.91 TFLOPS | 257 GFLOPS | |
| Peak SP performance | 8.73 TFLOPS | 8228 GFLOPS | 691Gflops |
GPU architecture vs CPU architecture.
* GPUs contain 100s of processing cores on a single card; several cards can fit in a desktop PC
* Each core carries out the same operations in parallel on different input data – single program, multiple data (SPMD) paradigm
* Extremely high arithmetic intensity if one can transfer the data onto and results off of the processors quickly
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GPU support by Julia is under active development. Check JuliaGPU for currently available packages.
There are multiple paradigms to program GPU in Julia, depending on the specific hardware.
CUDA is an ecosystem exclusively for Nvidia GPUs. There are extensive CUDA libraries for scientific computing: CuBLAS, CuRAND, CuSparse, CuSolve, CuDNN, …
The CUDA.jl package allows defining arrays on Nvidia GPUs and overloads many common operations.
The AMDGPU.jl package allows defining arrays on AMD GPUs and overloads many common operations.
The Metal.jl package allows defining arrays on Apple Silicon and overloads many common operations.
The oneAPI.jl package allows defining arrays on Intel GPUs and overloads many common operations.
I’ll illustrate using Metal.jl on my MacBook Pro running MacOS Ventura 13.2.1. It has Apple M2 chip with 38 GPU cores.
versioninfo()Julia Version 1.8.5
Commit 17cfb8e65ea (2023-01-08 06:45 UTC)
Platform Info:
OS: macOS (arm64-apple-darwin21.5.0)
CPU: 12 × Apple M2 Max
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-13.0.1 (ORCJIT, apple-m1)
Threads: 8 on 8 virtual cores
Environment:
JULIA_NUM_THREADS = 8
JULIA_EDITOR = codeLoad packages:
using Pkg
Pkg.activate(pwd())
Pkg.instantiate()
Pkg.status() Activating project at `~/Documents/github.com/ucla-biostat-257/2023spring/slides/09-juliagpu`Status `~/Documents/github.com/ucla-biostat-257/2023spring/slides/09-juliagpu/Project.toml`
[6e4b80f9] BenchmarkTools v1.3.2
[dde4c033] Metal v0.3.0
[37e2e46d] LinearAlgebrausing Metal
Metal.versioninfo()macOS 13.3.0, Darwin 21.5.0
Toolchain:
- Julia: 1.8.5
- LLVM: 13.0.1
1 device:
- Apple M2 Max (64.000 KiB allocated)# generate data on CPU
x = rand(Float32, 3, 3)
# transfer data form CPU to GPU
xd = MtlArray(x)3×3 MtlMatrix{Float32}:
0.631541 0.846448 0.379895
0.813597 0.999113 0.253971
0.0469926 0.179086 0.98002# generate array on GPU directly
# yd = Metal.ones(3, 3)
yd = MtlArray(ones(Float32, 3, 3))3×3 MtlMatrix{Float32}:
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0# collect data from GPU to CPU
x = collect(xd)3×3 Matrix{Float32}:
0.631541 0.846448 0.379895
0.813597 0.999113 0.253971
0.0469926 0.179086 0.98002using BenchmarkTools, LinearAlgebra, Random
Random.seed!(257)
n = 2^14
# on CPU
x = rand(Float32, n, n)
y = rand(Float32, n, n)
z = zeros(Float32, n, n)
# on GPU
xd = MtlArray(x)
yd = MtlArray(y)
zd = MtlArray(z)
# SP matrix multiplication on GPU
bm_gpu = @benchmark Metal.@sync mul!($zd, $xd, $yd)BenchmarkTools.Trial: 6 samples with 1 evaluation. Range (min … max): 899.295 ms … 908.975 ms ┊ GC (min … max): 0.00% … 0.00% Time (median): 900.655 ms ┊ GC (median): 0.00% Time (mean ± σ): 902.037 ms ± 3.630 ms ┊ GC (mean ± σ): 0.00% ± 0.00% █ █ █ █ █ █ █▁█▁▁▁█▁▁▁█▁▁▁▁▁▁▁▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁ 899 ms Histogram: frequency by time 909 ms < Memory estimate: 800 bytes, allocs estimate: 40.
We see GPU (this problem size on this machine) achieves a staggering 9 TGLOPS throughput with single precision!
# SP throughput on GPU
(2n^3) / (minimum(bm_gpu.times) / 1e9)9.78109311367398e12# SP matrix multiplication on CPU
bm_cpu = @benchmark mul!($z, $x, $y)BenchmarkTools.Trial: 1 sample with 1 evaluation. Single result which took 12.491 s (0.00% GC) to evaluate, with a memory estimate of 0 bytes, over 0 allocations.
# SP throughput on CPU
(2n^3) / (minimum(bm_cpu.times) / 1e9)7.041877507800785e11We see >10x speedup by GPUs in this matrix multiplication example.
# cholesky on Gram matrix
# This one doesn't seem to work on Apple M2 chip yet
# xtxd = xd'xd + I
# @benchmark Metal.@sync cholesky($(xtxd))# xtx = collect(xtxd)
# @benchmark cholesky($(Symmetric(xtx)))GPU speedup of Cholesky seems unavailable at the moment.
# elementwise function on GPU arrays
fill!(yd, 1)
bm_gpu = @benchmark Metal.@sync $zd .= log.($yd .+ sin.($xd))
bm_gpuBenchmarkTools.Trial: 125 samples with 1 evaluation. Range (min … max): 39.877 ms … 52.636 ms ┊ GC (min … max): 0.00% … 0.00% Time (median): 39.904 ms ┊ GC (median): 0.00% Time (mean ± σ): 40.009 ms ± 1.139 ms ┊ GC (mean ± σ): 0.00% ± 0.00% ▁ ▇█▅▄▂ ▅ ▄▁▁ ▅▃▁▁▅▁▃▆██▅▆█████▆████████▆▁▅▅▃▃▃▃▁▁▃▃▁▁▃▃▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃ ▃ 39.9 ms Histogram: frequency by time 40 ms < Memory estimate: 8.13 KiB, allocs estimate: 310.
# elementwise function on CPU arrays
x, y, z = collect(xd), collect(yd), collect(zd)
bm_cpu = @benchmark $z .= log.($y .+ sin.($x))
bm_cpuBenchmarkTools.Trial: 3 samples with 1 evaluation. Range (min … max): 2.373 s … 2.422 s ┊ GC (min … max): 0.00% … 0.00% Time (median): 2.407 s ┊ GC (median): 0.00% Time (mean ± σ): 2.401 s ± 24.741 ms ┊ GC (mean ± σ): 0.00% ± 0.00% █ █ █ █▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁ 2.37 s Histogram: frequency by time 2.42 s < Memory estimate: 0 bytes, allocs estimate: 0.
# Speed up
median(bm_cpu.times) / median(bm_gpu.times)60.33024155872633GPU brings great speedup (>50x) to the massive evaluation of elementary math functions.